Question: Solve for $x$ and $y$ using elimination. ${2x+6y = 38}$ ${-2x-5y = -33}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {2x+6y = 38}\thinspace$ to find $x$ ${2x + 6}{(5)}{= 38}$ $2x+30 = 38$ $2x+30{-30} = 38{-30}$ $2x = 8$ $\dfrac{2x}{{2}} = \dfrac{8}{{2}}$ ${x = 4}$ You can also plug ${y = 5}$ into $\thinspace {-2x-5y = -33}\thinspace$ and get the same answer for $x$ : ${-2x - 5}{(5)}{= -33}$ ${x = 4}$